LMFDB - Embedded newform 90.6.c.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,6,Mod(19,90)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("90.19");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	90.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.4345437832$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	90.19
Dual form			90.6.c.a.19.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} -16.0000 q^{4} +(-55.0000 - 10.0000i) q^{5} -158.000i q^{7} +64.0000i q^{8} +O(q^{10})$	\(q-4.00000i q^{2} -16.0000 q^{4} +(-55.0000 - 10.0000i) q^{5} -158.000i q^{7} +64.0000i q^{8} +(-40.0000 + 220.000i) q^{10} +148.000 q^{11} +684.000i q^{13} -632.000 q^{14} +256.000 q^{16} +2048.00i q^{17} -2220.00 q^{19} +(880.000 + 160.000i) q^{20} -592.000i q^{22} +1246.00i q^{23} +(2925.00 + 1100.00i) q^{25} +2736.00 q^{26} +2528.00i q^{28} -270.000 q^{29} -2048.00 q^{31} -1024.00i q^{32} +8192.00 q^{34} +(-1580.00 + 8690.00i) q^{35} +4372.00i q^{37} +8880.00i q^{38} +(640.000 - 3520.00i) q^{40} +2398.00 q^{41} +2294.00i q^{43} -2368.00 q^{44} +4984.00 q^{46} -10682.0i q^{47} -8157.00 q^{49} +(4400.00 - 11700.0i) q^{50} -10944.0i q^{52} -2964.00i q^{53} +(-8140.00 - 1480.00i) q^{55} +10112.0 q^{56} +1080.00i q^{58} -39740.0 q^{59} -42298.0 q^{61} +8192.00i q^{62} -4096.00 q^{64} +(6840.00 - 37620.0i) q^{65} -32098.0i q^{67} -32768.0i q^{68} +(34760.0 + 6320.00i) q^{70} +4248.00 q^{71} +30104.0i q^{73} +17488.0 q^{74} +35520.0 q^{76} -23384.0i q^{77} -35280.0 q^{79} +(-14080.0 - 2560.00i) q^{80} -9592.00i q^{82} +27826.0i q^{83} +(20480.0 - 112640. i) q^{85} +9176.00 q^{86} +9472.00i q^{88} -85210.0 q^{89} +108072. q^{91} -19936.0i q^{92} -42728.0 q^{94} +(122100. + 22200.0i) q^{95} +97232.0i q^{97} +32628.0i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{4} - 110 q^{5}+O(q^{10}) $ 2 * q - 32 * q^4 - 110 * q^5	$ 2 q - 32 q^{4} - 110 q^{5} - 80 q^{10} + 296 q^{11} - 1264 q^{14} + 512 q^{16} - 4440 q^{19} + 1760 q^{20} + 5850 q^{25} + 5472 q^{26} - 540 q^{29} - 4096 q^{31} + 16384 q^{34} - 3160 q^{35} + 1280 q^{40} + 4796 q^{41} - 4736 q^{44} + 9968 q^{46} - 16314 q^{49} + 8800 q^{50} - 16280 q^{55} + 20224 q^{56} - 79480 q^{59} - 84596 q^{61} - 8192 q^{64} + 13680 q^{65} + 69520 q^{70} + 8496 q^{71} + 34976 q^{74} + 71040 q^{76} - 70560 q^{79} - 28160 q^{80} + 40960 q^{85} + 18352 q^{86} - 170420 q^{89} + 216144 q^{91} - 85456 q^{94} + 244200 q^{95}+O(q^{100}) $ 2 * q - 32 * q^4 - 110 * q^5 - 80 * q^10 + 296 * q^11 - 1264 * q^14 + 512 * q^16 - 4440 * q^19 + 1760 * q^20 + 5850 * q^25 + 5472 * q^26 - 540 * q^29 - 4096 * q^31 + 16384 * q^34 - 3160 * q^35 + 1280 * q^40 + 4796 * q^41 - 4736 * q^44 + 9968 * q^46 - 16314 * q^49 + 8800 * q^50 - 16280 * q^55 + 20224 * q^56 - 79480 * q^59 - 84596 * q^61 - 8192 * q^64 + 13680 * q^65 + 69520 * q^70 + 8496 * q^71 + 34976 * q^74 + 71040 * q^76 - 70560 * q^79 - 28160 * q^80 + 40960 * q^85 + 18352 * q^86 - 170420 * q^89 + 216144 * q^91 - 85456 * q^94 + 244200 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−16.0000			−0.500000
$5$	−55.0000	−	10.0000i	−0.983870	−	0.178885i
$5$	−55.0000	−	10.0000i	−0.983870	−	0.178885i
$6$		0			0
$7$		−	158.000i		−	1.21874i	−0.792885	−	0.609371i	$-0.791422\pi$
$7$		−	158.000i		−	1.21874i	0.792885	−	0.609371i	$-0.208578\pi$
$8$			64.0000i			0.353553i
$9$		0			0
$10$	−40.0000	+	220.000i	−0.126491	+	0.695701i
$11$	148.000			0.368791			0.184395	−	0.982852i	$-0.440967\pi$
$11$	148.000			0.368791			0.184395	+	0.982852i	$0.440967\pi$
$12$		0			0
$13$			684.000i			1.12253i	0.827636	+	0.561265i	$0.189685\pi$
$13$			684.000i			1.12253i	−0.827636	+	0.561265i	$0.810315\pi$
$14$	−632.000			−0.861781
$15$		0			0
$16$	256.000			0.250000
$17$			2048.00i			1.71873i	0.511363	+	0.859365i	$0.329141\pi$
$17$			2048.00i			1.71873i	−0.511363	+	0.859365i	$0.670859\pi$
$18$		0			0
$19$	−2220.00			−1.41081			−0.705406	−	0.708804i	$-0.749235\pi$
$19$	−2220.00			−1.41081			−0.705406	+	0.708804i	$0.749235\pi$
$20$	880.000	+	160.000i	0.491935	+	0.0894427i
$21$		0			0
$22$		−	592.000i		−	0.260774i
$23$			1246.00i			0.491132i	0.969380	+	0.245566i	$0.0789738\pi$
$23$			1246.00i			0.491132i	−0.969380	+	0.245566i	$0.921026\pi$
$24$		0			0
$25$	2925.00	+	1100.00i	0.936000	+	0.352000i
$26$	2736.00			0.793748
$27$		0			0
$28$			2528.00i			0.609371i
$29$	−270.000			−0.0596168			−0.0298084	−	0.999556i	$-0.509490\pi$
$29$	−270.000			−0.0596168			−0.0298084	+	0.999556i	$0.509490\pi$
$30$		0			0
$31$	−2048.00			−0.382759			−0.191380	−	0.981516i	$-0.561296\pi$
$31$	−2048.00			−0.382759			−0.191380	+	0.981516i	$0.561296\pi$
$32$		−	1024.00i		−	0.176777i
$33$		0			0
$34$	8192.00			1.21533
$35$	−1580.00	+	8690.00i	−0.218015	+	1.19908i
$36$		0			0
$37$			4372.00i			0.525020i	0.964929	+	0.262510i	$0.0845503\pi$
$37$			4372.00i			0.525020i	−0.964929	+	0.262510i	$0.915450\pi$
$38$			8880.00i			0.997594i
$39$		0			0
$40$	640.000	−	3520.00i	0.0632456	−	0.347851i
$41$	2398.00			0.222787			0.111393	−	0.993776i	$-0.464469\pi$
$41$	2398.00			0.222787			0.111393	+	0.993776i	$0.464469\pi$
$42$		0			0
$43$			2294.00i			0.189200i	0.995515	+	0.0946002i	$0.0301573\pi$
$43$			2294.00i			0.189200i	−0.995515	+	0.0946002i	$0.969843\pi$
$44$	−2368.00			−0.184395
$45$		0			0
$46$	4984.00			0.347283
$47$		−	10682.0i		−	0.705355i	−0.935745	−	0.352678i	$-0.885271\pi$
$47$		−	10682.0i		−	0.705355i	0.935745	−	0.352678i	$-0.114729\pi$
$48$		0			0
$49$	−8157.00			−0.485333
$50$	4400.00	−	11700.0i	0.248902	−	0.661852i
$51$		0			0
$52$		−	10944.0i		−	0.561265i
$53$		−	2964.00i		−	0.144940i	−0.997371	−	0.0724700i	$-0.976912\pi$
$53$		−	2964.00i		−	0.144940i	0.997371	−	0.0724700i	$-0.0230882\pi$
$54$		0			0
$55$	−8140.00	−	1480.00i	−0.362842	−	0.0659713i
$56$	10112.0			0.430891
$57$		0			0
$58$			1080.00i			0.0421555i
$59$	−39740.0			−1.48627			−0.743135	−	0.669141i	$-0.766662\pi$
$59$	−39740.0			−1.48627			−0.743135	+	0.669141i	$0.766662\pi$
$60$		0			0
$61$	−42298.0			−1.45544			−0.727722	−	0.685873i	$-0.759421\pi$
$61$	−42298.0			−1.45544			−0.727722	+	0.685873i	$0.759421\pi$
$62$			8192.00i			0.270652i
$63$		0			0
$64$	−4096.00			−0.125000
$65$	6840.00	−	37620.0i	0.200804	−	1.10442i
$66$		0			0
$67$		−	32098.0i		−	0.873556i	−0.899569	−	0.436778i	$-0.856119\pi$
$67$		−	32098.0i		−	0.873556i	0.899569	−	0.436778i	$-0.143881\pi$
$68$		−	32768.0i		−	0.859365i
$69$		0			0
$70$	34760.0	+	6320.00i	0.847881	+	0.154160i
$71$	4248.00			0.100009			0.0500044	−	0.998749i	$-0.484076\pi$
$71$	4248.00			0.100009			0.0500044	+	0.998749i	$0.484076\pi$
$72$		0			0
$73$			30104.0i			0.661176i	0.943775	+	0.330588i	$0.107247\pi$
$73$			30104.0i			0.661176i	−0.943775	+	0.330588i	$0.892753\pi$
$74$	17488.0			0.371245
$75$		0			0
$76$	35520.0			0.705406
$77$		−	23384.0i		−	0.449461i
$78$		0			0
$79$	−35280.0			−0.636005			−0.318003	−	0.948090i	$-0.603012\pi$
$79$	−35280.0			−0.636005			−0.318003	+	0.948090i	$0.603012\pi$
$80$	−14080.0	−	2560.00i	−0.245967	−	0.0447214i
$81$		0			0
$82$		−	9592.00i		−	0.157534i
$83$			27826.0i			0.443359i	0.975120	+	0.221680i	$0.0711539\pi$
$83$			27826.0i			0.443359i	−0.975120	+	0.221680i	$0.928846\pi$
$84$		0			0
$85$	20480.0	−	112640.i	0.307456	−	1.69101i
$86$	9176.00			0.133785
$87$		0			0
$88$			9472.00i			0.130387i
$89$	−85210.0			−1.14029			−0.570145	−	0.821544i	$-0.693113\pi$
$89$	−85210.0			−1.14029			−0.570145	+	0.821544i	$0.693113\pi$
$90$		0			0
$91$	108072.			1.36807
$92$		−	19936.0i		−	0.245566i
$93$		0			0
$94$	−42728.0			−0.498762
$95$	122100.	+	22200.0i	1.38805	+	0.252374i
$96$		0			0
$97$			97232.0i			1.04925i	0.851333	+	0.524626i	$0.175795\pi$
$97$			97232.0i			1.04925i	−0.851333	+	0.524626i	$0.824205\pi$
$98$			32628.0i			0.343183i
$99$		0			0
$100$	−46800.0	−	17600.0i	−0.468000	−	0.176000i
$101$	4298.00			0.0419240			0.0209620	−	0.999780i	$-0.493327\pi$
$101$	4298.00			0.0419240			0.0209620	+	0.999780i	$0.493327\pi$
$102$		0			0
$103$			124114.i			1.15273i	0.817192	+	0.576365i	$0.195529\pi$
$103$			124114.i			1.15273i	−0.817192	+	0.576365i	$0.804471\pi$
$104$	−43776.0			−0.396874
$105$		0			0
$106$	−11856.0			−0.102488
$107$		−	42342.0i		−	0.357530i	−0.983892	−	0.178765i	$-0.942790\pi$
$107$		−	42342.0i		−	0.357530i	0.983892	−	0.178765i	$-0.0572101\pi$
$108$		0			0
$109$	35990.0			0.290145			0.145073	−	0.989421i	$-0.453658\pi$
$109$	35990.0			0.290145			0.145073	+	0.989421i	$0.453658\pi$
$110$	−5920.00	+	32560.0i	−0.0466487	+	0.256568i
$111$		0			0
$112$		−	40448.0i		−	0.304686i
$113$			228816.i			1.68574i	0.538118	+	0.842869i	$0.319135\pi$
$113$			228816.i			1.68574i	−0.538118	+	0.842869i	$0.680865\pi$
$114$		0			0
$115$	12460.0	−	68530.0i	0.0878564	−	0.483210i
$116$	4320.00			0.0298084
$117$		0			0
$118$			158960.i			1.05095i
$119$	323584.			2.09469
$120$		0			0
$121$	−139147.			−0.863993
$122$			169192.i			1.02915i
$123$		0			0
$124$	32768.0			0.191380
$125$	−149875.	−	89750.0i	−0.857935	−	0.513759i
$126$		0			0
$127$		−	175238.i		−	0.964093i	−0.876146	−	0.482047i	$-0.839894\pi$
$127$		−	175238.i		−	0.964093i	0.876146	−	0.482047i	$-0.160106\pi$
$128$			16384.0i			0.0883883i
$129$		0			0
$130$	−150480.	−	27360.0i	−0.780945	−	0.141990i
$131$	−299652.			−1.52559			−0.762797	−	0.646638i	$-0.776174\pi$
$131$	−299652.			−1.52559			−0.762797	+	0.646638i	$0.776174\pi$
$132$		0			0
$133$			350760.i			1.71942i
$134$	−128392.			−0.617698
$135$		0			0
$136$	−131072.			−0.607663
$137$			107928.i			0.491284i	0.969361	+	0.245642i	$0.0789988\pi$
$137$			107928.i			0.491284i	−0.969361	+	0.245642i	$0.921001\pi$
$138$		0			0
$139$	196460.			0.862456			0.431228	−	0.902243i	$-0.358080\pi$
$139$	196460.			0.862456			0.431228	+	0.902243i	$0.358080\pi$
$140$	25280.0	−	139040.i	0.109008	−	0.599542i
$141$		0			0
$142$		−	16992.0i		−	0.0707170i
$143$			101232.i			0.413978i
$144$		0			0
$145$	14850.0	+	2700.00i	0.0586552	+	0.0106646i
$146$	120416.			0.467522
$147$		0			0
$148$		−	69952.0i		−	0.262510i
$149$	138850.			0.512366			0.256183	−	0.966628i	$-0.417535\pi$
$149$	138850.			0.512366			0.256183	+	0.966628i	$0.417535\pi$
$150$		0			0
$151$	416152.			1.48528			0.742642	−	0.669688i	$-0.233572\pi$
$151$	416152.			1.48528			0.742642	+	0.669688i	$0.233572\pi$
$152$		−	142080.i		−	0.498797i
$153$		0			0
$154$	−93536.0			−0.317817
$155$	112640.	+	20480.0i	0.376585	+	0.0684701i
$156$		0			0
$157$		−	433108.i		−	1.40232i	−0.713004	−	0.701160i	$-0.752666\pi$
$157$		−	433108.i		−	1.40232i	0.713004	−	0.701160i	$-0.247334\pi$
$158$			141120.i			0.449724i
$159$		0			0
$160$	−10240.0	+	56320.0i	−0.0316228	+	0.173925i
$161$	196868.			0.598564
$162$		0			0
$163$			149134.i			0.439651i	0.975539	+	0.219825i	$0.0705487\pi$
$163$			149134.i			0.439651i	−0.975539	+	0.219825i	$0.929451\pi$
$164$	−38368.0			−0.111393
$165$		0			0
$166$	111304.			0.313502
$167$		−	559602.i		−	1.55270i	−0.630301	−	0.776351i	$-0.717068\pi$
$167$		−	559602.i		−	1.55270i	0.630301	−	0.776351i	$-0.282932\pi$
$168$		0			0
$169$	−96563.0			−0.260072
$170$	−450560.	−	81920.0i	−1.19572	−	0.217404i
$171$		0			0
$172$		−	36704.0i		−	0.0946002i
$173$		−	343804.i		−	0.873365i	−0.899616	−	0.436682i	$-0.856153\pi$
$173$		−	343804.i		−	0.873365i	0.899616	−	0.436682i	$-0.143847\pi$
$174$		0			0
$175$	173800.	−	462150.i	0.428997	−	1.14074i
$176$	37888.0			0.0921977
$177$		0			0
$178$			340840.i			0.806307i
$179$	23980.0			0.0559392			0.0279696	−	0.999609i	$-0.491096\pi$
$179$	23980.0			0.0559392			0.0279696	+	0.999609i	$0.491096\pi$
$180$		0			0
$181$	−651898.			−1.47905			−0.739526	−	0.673128i	$-0.764950\pi$
$181$	−651898.			−1.47905			−0.739526	+	0.673128i	$0.764950\pi$
$182$		−	432288.i		−	0.967375i
$183$		0			0
$184$	−79744.0			−0.173641
$185$	43720.0	−	240460.i	0.0939184	−	0.516551i
$186$		0			0
$187$			303104.i			0.633852i
$188$			170912.i			0.352678i
$189$		0			0
$190$	88800.0	−	488400.i	0.178455	−	0.981503i
$191$	−202752.			−0.402144			−0.201072	−	0.979576i	$-0.564443\pi$
$191$	−202752.			−0.402144			−0.201072	+	0.979576i	$0.564443\pi$
$192$		0			0
$193$		−	452656.i		−	0.874732i	−0.899284	−	0.437366i	$-0.855911\pi$
$193$		−	452656.i		−	0.874732i	0.899284	−	0.437366i	$-0.144089\pi$
$194$	388928.			0.741933
$195$		0			0
$196$	130512.			0.242667
$197$			337468.i			0.619537i	0.950812	+	0.309768i	$0.100252\pi$
$197$			337468.i			0.619537i	−0.950812	+	0.309768i	$0.899748\pi$
$198$		0			0
$199$	561000.			1.00422			0.502112	−	0.864803i	$-0.332557\pi$
$199$	561000.			1.00422			0.502112	+	0.864803i	$0.332557\pi$
$200$	−70400.0	+	187200.i	−0.124451	+	0.330926i
$201$		0			0
$202$		−	17192.0i		−	0.0296448i
$203$			42660.0i			0.0726576i
$204$		0			0
$205$	−131890.	−	23980.0i	−0.219193	−	0.0398533i
$206$	496456.			0.815103
$207$		0			0
$208$			175104.i			0.280632i
$209$	−328560.			−0.520294
$210$		0			0
$211$	−805548.			−1.24562			−0.622810	−	0.782373i	$-0.714009\pi$
$211$	−805548.			−1.24562			−0.622810	+	0.782373i	$0.714009\pi$
$212$			47424.0i			0.0724700i
$213$		0			0
$214$	−169368.			−0.252812
$215$	22940.0	−	126170.i	0.0338452	−	0.186149i
$216$		0			0
$217$			323584.i			0.466485i
$218$		−	143960.i		−	0.205164i
$219$		0			0
$220$	130240.	+	23680.0i	0.181421	+	0.0329856i
$221$	−1.40083e6			−1.92932
$222$		0			0
$223$			1.21855e6i			1.64090i	0.571717	+	0.820451i	$0.306278\pi$
$223$			1.21855e6i			1.64090i	−0.571717	+	0.820451i	$0.693722\pi$
$224$	−161792.			−0.215445
$225$		0			0
$226$	915264.			1.19200
$227$			564338.i			0.726900i	0.931614	+	0.363450i	$0.118401\pi$
$227$			564338.i			0.726900i	−0.931614	+	0.363450i	$0.881599\pi$
$228$		0			0
$229$	−560330.			−0.706082			−0.353041	−	0.935608i	$-0.614852\pi$
$229$	−560330.			−0.706082			−0.353041	+	0.935608i	$0.614852\pi$
$230$	−274120.	−	49840.0i	−0.341681	−	0.0621239i
$231$		0			0
$232$		−	17280.0i		−	0.0210777i
$233$			293576.i			0.354267i	0.984187	+	0.177134i	$0.0566824\pi$
$233$			293576.i			0.354267i	−0.984187	+	0.177134i	$0.943318\pi$
$234$		0			0
$235$	−106820.	+	587510.i	−0.126178	+	0.693978i
$236$	635840.			0.743135
$237$		0			0
$238$		−	1.29434e6i		−	1.48117i
$239$	584240.			0.661602			0.330801	−	0.943701i	$-0.392681\pi$
$239$	584240.			0.661602			0.330801	+	0.943701i	$0.392681\pi$
$240$		0			0
$241$	−563798.			−0.625289			−0.312645	−	0.949870i	$-0.601215\pi$
$241$	−563798.			−0.625289			−0.312645	+	0.949870i	$0.601215\pi$
$242$			556588.i			0.610936i
$243$		0			0
$244$	676768.			0.727722
$245$	448635.	+	81570.0i	0.477505	+	0.0868191i
$246$		0			0
$247$		−	1.51848e6i		−	1.58368i
$248$		−	131072.i		−	0.135326i
$249$		0			0
$250$	−359000.	+	599500.i	−0.363282	+	0.606651i
$251$	1.01975e6			1.02167			0.510833	−	0.859680i	$-0.329337\pi$
$251$	1.01975e6			1.02167			0.510833	+	0.859680i	$0.329337\pi$
$252$		0			0
$253$			184408.i			0.181125i
$254$	−700952.			−0.681717
$255$		0			0
$256$	65536.0			0.0625000
$257$			657408.i			0.620872i	0.950594	+	0.310436i	$0.100475\pi$
$257$			657408.i			0.620872i	−0.950594	+	0.310436i	$0.899525\pi$
$258$		0			0
$259$	690776.			0.639864
$260$	−109440.	+	601920.i	−0.100402	+	0.552211i
$261$		0			0
$262$			1.19861e6i			1.07876i
$263$			562366.i			0.501337i	0.968073	+	0.250668i	$0.0806504\pi$
$263$			562366.i			0.501337i	−0.968073	+	0.250668i	$0.919350\pi$
$264$		0			0
$265$	−29640.0	+	163020.i	−0.0259277	+	0.142602i
$266$	1.40304e6			1.21581
$267$		0			0
$268$			513568.i			0.436778i
$269$	366570.			0.308870			0.154435	−	0.988003i	$-0.450644\pi$
$269$	366570.			0.308870			0.154435	+	0.988003i	$0.450644\pi$
$270$		0			0
$271$	1.16075e6			0.960099			0.480050	−	0.877241i	$-0.340619\pi$
$271$	1.16075e6			0.960099			0.480050	+	0.877241i	$0.340619\pi$
$272$			524288.i			0.429682i
$273$		0			0
$274$	431712.			0.347390
$275$	432900.	+	162800.i	0.345188	+	0.129814i
$276$		0			0
$277$			2.51501e6i			1.96943i	0.174172	+	0.984715i	$0.444275\pi$
$277$			2.51501e6i			1.96943i	−0.174172	+	0.984715i	$0.555725\pi$
$278$		−	785840.i		−	0.609849i
$279$		0			0
$280$	−556160.	−	101120.i	−0.423940	−	0.0770800i
$281$	−2.08600e6			−1.57597			−0.787987	−	0.615692i	$-0.788876\pi$
$281$	−2.08600e6			−1.57597			−0.787987	+	0.615692i	$0.788876\pi$
$282$		0			0
$283$		−	2.23803e6i		−	1.66111i	−0.556935	−	0.830556i	$-0.688023\pi$
$283$		−	2.23803e6i		−	1.66111i	0.556935	−	0.830556i	$-0.311977\pi$
$284$	−67968.0			−0.0500044
$285$		0			0
$286$	404928.			0.292727
$287$		−	378884.i		−	0.271520i
$288$		0			0
$289$	−2.77445e6			−1.95403
$290$	10800.0	−	59400.0i	0.00754100	−	0.0414755i
$291$		0			0
$292$		−	481664.i		−	0.330588i
$293$			975756.i			0.664006i	0.943278	+	0.332003i	$0.107724\pi$
$293$			975756.i			0.664006i	−0.943278	+	0.332003i	$0.892276\pi$
$294$		0			0
$295$	2.18570e6	+	397400.i	1.46230	+	0.265872i
$296$	−279808.			−0.185623
$297$		0			0
$298$		−	555400.i		−	0.362297i
$299$	−852264.			−0.551310
$300$		0			0
$301$	362452.			0.230587
$302$		−	1.66461e6i		−	1.05025i
$303$		0			0
$304$	−568320.			−0.352703
$305$	2.32639e6	+	422980.i	1.43197	+	0.260358i
$306$		0			0
$307$		−	87858.0i		−	0.0532029i	−0.999646	−	0.0266015i	$-0.991531\pi$
$307$		−	87858.0i		−	0.0532029i	0.999646	−	0.0266015i	$-0.00846850\pi$
$308$			374144.i			0.224730i
$309$		0			0
$310$	81920.0	−	450560.i	0.0484156	−	0.266286i
$311$	−599352.			−0.351383			−0.175692	−	0.984445i	$-0.556216\pi$
$311$	−599352.			−0.351383			−0.175692	+	0.984445i	$0.556216\pi$
$312$		0			0
$313$		−	2.09342e6i		−	1.20780i	−0.797060	−	0.603900i	$-0.793613\pi$
$313$		−	2.09342e6i		−	1.20780i	0.797060	−	0.603900i	$-0.206387\pi$
$314$	−1.73243e6			−0.991590
$315$		0			0
$316$	564480.			0.318003
$317$		−	2.41625e6i		−	1.35050i	−0.737590	−	0.675249i	$-0.764036\pi$
$317$		−	2.41625e6i		−	1.35050i	0.737590	−	0.675249i	$-0.235964\pi$
$318$		0			0
$319$	−39960.0			−0.0219861
$320$	225280.	+	40960.0i	0.122984	+	0.0223607i
$321$		0			0
$322$		−	787472.i		−	0.423249i
$323$		−	4.54656e6i		−	2.42480i
$324$		0			0
$325$	−752400.	+	2.00070e6i	−0.395130	+	1.05069i
$326$	596536.			0.310880
$327$		0			0
$328$			153472.i			0.0787670i
$329$	−1.68776e6			−0.859647
$330$		0			0
$331$	−1.64095e6			−0.823237			−0.411618	−	0.911356i	$-0.635036\pi$
$331$	−1.64095e6			−0.823237			−0.411618	+	0.911356i	$0.635036\pi$
$332$		−	445216.i		−	0.221680i
$333$		0			0
$334$	−2.23841e6			−1.09793
$335$	−320980.	+	1.76539e6i	−0.156267	+	0.859466i
$336$		0			0
$337$		−	2.18773e6i		−	1.04935i	−0.851304	−	0.524673i	$-0.824188\pi$
$337$		−	2.18773e6i		−	1.04935i	0.851304	−	0.524673i	$-0.175812\pi$
$338$			386252.i			0.183899i
$339$		0			0
$340$	−327680.	+	1.80224e6i	−0.153728	+	0.845503i
$341$	−303104.			−0.141158
$342$		0			0
$343$		−	1.36670e6i		−	0.627246i
$344$	−146816.			−0.0668925
$345$		0			0
$346$	−1.37522e6			−0.617562
$347$			2.74502e6i			1.22383i	0.790923	+	0.611916i	$0.209601\pi$
$347$			2.74502e6i			1.22383i	−0.790923	+	0.611916i	$0.790399\pi$
$348$		0			0
$349$	2.65115e6			1.16512			0.582560	−	0.812788i	$-0.302051\pi$
$349$	2.65115e6			1.16512			0.582560	+	0.812788i	$0.302051\pi$
$350$	−1.84860e6	−	695200.i	−0.806627	−	0.303347i
$351$		0			0
$352$		−	151552.i		−	0.0651936i
$353$		−	3.05766e6i		−	1.30603i	−0.757345	−	0.653015i	$-0.773504\pi$
$353$		−	3.05766e6i		−	1.30603i	0.757345	−	0.653015i	$-0.226496\pi$
$354$		0			0
$355$	−233640.	−	42480.0i	−0.0983957	−	0.0178901i
$356$	1.36336e6			0.570145
$357$		0			0
$358$		−	95920.0i		−	0.0395550i
$359$	3.79356e6			1.55350			0.776749	−	0.629810i	$-0.216867\pi$
$359$	3.79356e6			1.55350			0.776749	+	0.629810i	$0.216867\pi$
$360$		0			0
$361$	2.45230e6			0.990389
$362$			2.60759e6i			1.04585i
$363$		0			0
$364$	−1.72915e6			−0.684037
$365$	301040.	−	1.65572e6i	0.118275	−	0.650511i
$366$		0			0
$367$			3.11060e6i			1.20553i	0.797917	+	0.602767i	$0.205935\pi$
$367$			3.11060e6i			1.20553i	−0.797917	+	0.602767i	$0.794065\pi$
$368$			318976.i			0.122783i
$369$		0			0
$370$	−961840.	−	174880.i	−0.365257	−	0.0664104i
$371$	−468312.			−0.176645
$372$		0			0
$373$		−	1.41520e6i		−	0.526677i	−0.964703	−	0.263339i	$-0.915176\pi$
$373$		−	1.41520e6i		−	0.526677i	0.964703	−	0.263339i	$-0.0848236\pi$
$374$	1.21242e6			0.448201
$375$		0			0
$376$	683648.			0.249381
$377$		−	184680.i		−	0.0669216i
$378$		0			0
$379$	3.90262e6			1.39559			0.697796	−	0.716297i	$-0.254164\pi$
$379$	3.90262e6			1.39559			0.697796	+	0.716297i	$0.254164\pi$
$380$	−1.95360e6	−	355200.i	−0.694027	−	0.126187i
$381$		0			0
$382$			811008.i			0.284359i
$383$		−	695674.i		−	0.242331i	−0.992632	−	0.121165i	$-0.961337\pi$
$383$		−	695674.i		−	0.242331i	0.992632	−	0.121165i	$-0.0386632\pi$
$384$		0			0
$385$	−233840.	+	1.28612e6i	−0.0804020	+	0.442211i
$386$	−1.81062e6			−0.618529
$387$		0			0
$388$		−	1.55571e6i		−	0.524626i
$389$	498290.			0.166958			0.0834792	−	0.996510i	$-0.473397\pi$
$389$	498290.			0.166958			0.0834792	+	0.996510i	$0.473397\pi$
$390$		0			0
$391$	−2.55181e6			−0.844124
$392$		−	522048.i		−	0.171591i
$393$		0			0
$394$	1.34987e6			0.438079
$395$	1.94040e6	+	352800.i	0.625747	+	0.113772i
$396$		0			0
$397$		−	1.09567e6i		−	0.348901i	−0.984666	−	0.174451i	$-0.944185\pi$
$397$		−	1.09567e6i		−	0.348901i	0.984666	−	0.174451i	$-0.0558150\pi$
$398$		−	2.24400e6i		−	0.710093i
$399$		0			0
$400$	748800.	+	281600.i	0.234000	+	0.0880000i
$401$	2.49160e6			0.773779			0.386890	−	0.922126i	$-0.373549\pi$
$401$	2.49160e6			0.773779			0.386890	+	0.922126i	$0.373549\pi$
$402$		0			0
$403$		−	1.40083e6i		−	0.429659i
$404$	−68768.0			−0.0209620
$405$		0			0
$406$	170640.			0.0513766
$407$			647056.i			0.193623i
$408$		0			0
$409$	3.63349e6			1.07403			0.537014	−	0.843573i	$-0.319552\pi$
$409$	3.63349e6			1.07403			0.537014	+	0.843573i	$0.319552\pi$
$410$	−95920.0	+	527560.i	−0.0281806	+	0.154993i
$411$		0			0
$412$		−	1.98582e6i		−	0.576365i
$413$			6.27892e6i			1.81138i
$414$		0			0
$415$	278260.	−	1.53043e6i	0.0793105	−	0.436208i
$416$	700416.			0.198437
$417$		0			0
$418$			1.31424e6i			0.367904i
$419$	−3.64378e6			−1.01395			−0.506976	−	0.861960i	$-0.669237\pi$
$419$	−3.64378e6			−1.01395			−0.506976	+	0.861960i	$0.669237\pi$
$420$		0			0
$421$	−1.82530e6			−0.501913			−0.250957	−	0.967998i	$-0.580745\pi$
$421$	−1.82530e6			−0.501913			−0.250957	+	0.967998i	$0.580745\pi$
$422$			3.22219e6i			0.880786i
$423$		0			0
$424$	189696.			0.0512441
$425$	−2.25280e6	+	5.99040e6i	−0.604993	+	1.60873i
$426$		0			0
$427$			6.68308e6i			1.77381i
$428$			677472.i			0.178765i
$429$		0			0
$430$	−504680.	−	91760.0i	−0.131627	−	0.0239322i
$431$	−2.85435e6			−0.740141			−0.370070	−	0.929004i	$-0.620666\pi$
$431$	−2.85435e6			−0.740141			−0.370070	+	0.929004i	$0.620666\pi$
$432$		0			0
$433$		−	587776.i		−	0.150658i	−0.997159	−	0.0753290i	$-0.975999\pi$
$433$		−	587776.i		−	0.150658i	0.997159	−	0.0753290i	$-0.0240007\pi$
$434$	1.29434e6			0.329855
$435$		0			0
$436$	−575840.			−0.145073
$437$		−	2.76612e6i		−	0.692895i
$438$		0			0
$439$	−6.11604e6			−1.51464			−0.757319	−	0.653045i	$-0.773491\pi$
$439$	−6.11604e6			−1.51464			−0.757319	+	0.653045i	$0.773491\pi$
$440$	94720.0	−	520960.i	0.0233244	−	0.128284i
$441$		0			0
$442$			5.60333e6i			1.36424i
$443$			2.35771e6i			0.570795i	0.958409	+	0.285398i	$0.0921257\pi$
$443$			2.35771e6i			0.570795i	−0.958409	+	0.285398i	$0.907874\pi$
$444$		0			0
$445$	4.68655e6	+	852100.i	1.12190	+	0.203981i
$446$	4.87422e6			1.16029
$447$		0			0
$448$			647168.i			0.152343i
$449$	5.49735e6			1.28688			0.643439	−	0.765497i	$-0.277507\pi$
$449$	5.49735e6			1.28688			0.643439	+	0.765497i	$0.277507\pi$
$450$		0			0
$451$	354904.			0.0821617
$452$		−	3.66106e6i		−	0.842869i
$453$		0			0
$454$	2.25735e6			0.513996
$455$	−5.94396e6	−	1.08072e6i	−1.34601	−	0.244729i
$456$		0			0
$457$			1.16039e6i			0.259905i	0.991520	+	0.129952i	$0.0414824\pi$
$457$			1.16039e6i			0.259905i	−0.991520	+	0.129952i	$0.958518\pi$
$458$			2.24132e6i			0.499275i
$459$		0			0
$460$	−199360.	+	1.09648e6i	−0.0439282	+	0.241605i
$461$	2.30330e6			0.504775			0.252387	−	0.967626i	$-0.418784\pi$
$461$	2.30330e6			0.504775			0.252387	+	0.967626i	$0.418784\pi$
$462$		0			0
$463$			2.71343e6i			0.588257i	0.955766	+	0.294128i	$0.0950293\pi$
$463$			2.71343e6i			0.588257i	−0.955766	+	0.294128i	$0.904971\pi$
$464$	−69120.0			−0.0149042
$465$		0			0
$466$	1.17430e6			0.250505
$467$			4.05050e6i			0.859441i	0.902962	+	0.429721i	$0.141388\pi$
$467$			4.05050e6i			0.859441i	−0.902962	+	0.429721i	$0.858612\pi$
$468$		0			0
$469$	−5.07148e6			−1.06464
$470$	2.35004e6	+	427280.i	0.490716	+	0.0892212i
$471$		0			0
$472$		−	2.54336e6i		−	0.525476i
$473$			339512.i			0.0697754i
$474$		0			0
$475$	−6.49350e6	−	2.44200e6i	−1.32052	−	0.496606i
$476$	−5.17734e6			−1.04734
$477$		0			0
$478$		−	2.33696e6i		−	0.467823i
$479$	5.60528e6			1.11624			0.558121	−	0.829759i	$-0.311522\pi$
$479$	5.60528e6			1.11624			0.558121	+	0.829759i	$0.311522\pi$
$480$		0			0
$481$	−2.99045e6			−0.589350
$482$			2.25519e6i			0.442146i
$483$		0			0
$484$	2.22635e6			0.431997
$485$	972320.	−	5.34776e6i	0.187696	−	1.03233i
$486$		0			0
$487$		−	7.13168e6i		−	1.36260i	−0.732003	−	0.681301i	$-0.761414\pi$
$487$		−	7.13168e6i		−	1.36260i	0.732003	−	0.681301i	$-0.238586\pi$
$488$		−	2.70707e6i		−	0.514577i
$489$		0			0
$490$	326280.	−	1.79454e6i	0.0613904	−	0.337647i
$491$	−5.88145e6			−1.10098			−0.550492	−	0.834841i	$-0.685560\pi$
$491$	−5.88145e6			−1.10098			−0.550492	+	0.834841i	$0.685560\pi$
$492$		0			0
$493$		−	552960.i		−	0.102465i
$494$	−6.07392e6			−1.11983
$495$		0			0
$496$	−524288.			−0.0956898
$497$		−	671184.i		−	0.121885i
$498$		0			0
$499$	−1.75710e6			−0.315897			−0.157948	−	0.987447i	$-0.550488\pi$
$499$	−1.75710e6			−0.315897			−0.157948	+	0.987447i	$0.550488\pi$
$500$	2.39800e6	+	1.43600e6i	0.428967	+	0.256879i
$501$		0			0
$502$		−	4.07899e6i		−	0.722426i
$503$		−	4.91411e6i		−	0.866015i	−0.901390	−	0.433007i	$-0.857452\pi$
$503$		−	4.91411e6i		−	0.866015i	0.901390	−	0.433007i	$-0.142548\pi$
$504$		0			0
$505$	−236390.	−	42980.0i	−0.0412478	−	0.00749960i
$506$	737632.			0.128075
$507$		0			0
$508$			2.80381e6i			0.482047i
$509$	−5.75499e6			−0.984578			−0.492289	−	0.870432i	$-0.663840\pi$
$509$	−5.75499e6			−0.984578			−0.492289	+	0.870432i	$0.663840\pi$
$510$		0			0
$511$	4.75643e6			0.805803
$512$		−	262144.i		−	0.0441942i
$513$		0			0
$514$	2.62963e6			0.439023
$515$	1.24114e6	−	6.82627e6i	0.206207	−	1.13414i
$516$		0			0
$517$		−	1.58094e6i		−	0.260128i
$518$		−	2.76310e6i		−	0.452452i
$519$		0			0
$520$	2.40768e6	+	437760.i	0.390472	+	0.0709950i
$521$	1.61980e6			0.261437			0.130718	−	0.991420i	$-0.458272\pi$
$521$	1.61980e6			0.261437			0.130718	+	0.991420i	$0.458272\pi$
$522$		0			0
$523$			1.19117e7i			1.90422i	0.305751	+	0.952112i	$0.401093\pi$
$523$			1.19117e7i			1.90422i	−0.305751	+	0.952112i	$0.598907\pi$
$524$	4.79443e6			0.762797
$525$		0			0
$526$	2.24946e6			0.354499
$527$		−	4.19430e6i		−	0.657860i
$528$		0			0
$529$	4.88383e6			0.758789
$530$	652080.	+	118560.i	0.100835	+	0.0183336i
$531$		0			0
$532$		−	5.61216e6i		−	0.859708i
$533$			1.64023e6i			0.250085i
$534$		0			0
$535$	−423420.	+	2.32881e6i	−0.0639568	+	0.351763i
$536$	2.05427e6			0.308849
$537$		0			0
$538$		−	1.46628e6i		−	0.218404i
$539$	−1.20724e6			−0.178986
$540$		0			0
$541$	4.07630e6			0.598788			0.299394	−	0.954130i	$-0.403215\pi$
$541$	4.07630e6			0.598788			0.299394	+	0.954130i	$0.403215\pi$
$542$		−	4.64301e6i		−	0.678893i
$543$		0			0
$544$	2.09715e6			0.303831
$545$	−1.97945e6	−	359900.i	−0.285465	−	0.0519028i
$546$		0			0
$547$		−	1.23680e7i		−	1.76739i	−0.468065	−	0.883694i	$-0.655049\pi$
$547$		−	1.23680e7i		−	1.76739i	0.468065	−	0.883694i	$-0.344951\pi$
$548$		−	1.72685e6i		−	0.245642i
$549$		0			0
$550$	651200.	−	1.73160e6i	0.0917926	−	0.244085i
$551$	599400.			0.0841081
$552$		0			0
$553$			5.57424e6i			0.775127i
$554$	1.00600e7			1.39260
$555$		0			0
$556$	−3.14336e6			−0.431228
$557$			130308.i			0.0177964i	0.999960	+	0.00889822i	$0.00283243\pi$
$557$			130308.i			0.0177964i	−0.999960	+	0.00889822i	$0.997168\pi$
$558$		0			0
$559$	−1.56910e6			−0.212383
$560$	−404480.	+	2.22464e6i	−0.0545038	+	0.299771i
$561$		0			0
$562$			8.34401e6i			1.11438i
$563$			5.91687e6i			0.786721i	0.919384	+	0.393361i	$0.128688\pi$
$563$			5.91687e6i			0.786721i	−0.919384	+	0.393361i	$0.871312\pi$
$564$		0			0
$565$	2.28816e6	−	1.25849e7i	0.301554	−	1.65855i
$566$	−8.95210e6			−1.17458
$567$		0			0
$568$			271872.i			0.0353585i
$569$	−9.03013e6			−1.16927			−0.584633	−	0.811298i	$-0.698761\pi$
$569$	−9.03013e6			−1.16927			−0.584633	+	0.811298i	$0.698761\pi$
$570$		0			0
$571$	−1.07093e7			−1.37459			−0.687294	−	0.726379i	$-0.741202\pi$
$571$	−1.07093e7			−1.37459			−0.687294	+	0.726379i	$0.741202\pi$
$572$		−	1.61971e6i		−	0.206989i
$573$		0			0
$574$	−1.51554e6			−0.191994
$575$	−1.37060e6	+	3.64455e6i	−0.172879	+	0.459700i
$576$		0			0
$577$			1.22051e6i			0.152617i	0.997084	+	0.0763084i	$0.0243134\pi$
$577$			1.22051e6i			0.152617i	−0.997084	+	0.0763084i	$0.975687\pi$
$578$			1.10978e7i			1.38171i
$579$		0			0
$580$	−237600.	−	43200.0i	−0.0293276	−	0.00533229i
$581$	4.39651e6			0.540341
$582$		0			0
$583$		−	438672.i		−	0.0534526i
$584$	−1.92666e6			−0.233761
$585$		0			0
$586$	3.90302e6			0.469523
$587$		−	1.47104e7i		−	1.76210i	−0.473026	−	0.881049i	$-0.656838\pi$
$587$		−	1.47104e7i		−	1.76210i	0.473026	−	0.881049i	$-0.343162\pi$
$588$		0			0
$589$	4.54656e6			0.540001
$590$	1.58960e6	−	8.74280e6i	0.188000	−	1.03400i
$591$		0			0
$592$			1.11923e6i			0.131255i
$593$		−	8.52014e6i		−	0.994970i	−0.867472	−	0.497485i	$-0.834257\pi$
$593$		−	8.52014e6i		−	0.994970i	0.867472	−	0.497485i	$-0.165743\pi$
$594$		0			0
$595$	−1.77971e7	−	3.23584e6i	−2.06090	−	0.374709i
$596$	−2.22160e6			−0.256183
$597$		0			0
$598$			3.40906e6i			0.389835i
$599$	2.90100e6			0.330355			0.165177	−	0.986264i	$-0.447180\pi$
$599$	2.90100e6			0.330355			0.165177	+	0.986264i	$0.447180\pi$
$600$		0			0
$601$	5.72760e6			0.646825			0.323412	−	0.946258i	$-0.395170\pi$
$601$	5.72760e6			0.646825			0.323412	+	0.946258i	$0.395170\pi$
$602$		−	1.44981e6i		−	0.163049i
$603$		0			0
$604$	−6.65843e6			−0.742642
$605$	7.65308e6	+	1.39147e6i	0.850057	+	0.154556i
$606$		0			0
$607$			8.79924e6i			0.969334i	0.874699	+	0.484667i	$0.161059\pi$
$607$			8.79924e6i			0.969334i	−0.874699	+	0.484667i	$0.838941\pi$
$608$			2.27328e6i			0.249399i
$609$		0			0
$610$	1.69192e6	−	9.30556e6i	0.184101	−	1.01255i
$611$	7.30649e6			0.791782
$612$		0			0
$613$			1.03408e6i			0.111149i	0.998455	+	0.0555744i	$0.0176990\pi$
$613$			1.03408e6i			0.111149i	−0.998455	+	0.0555744i	$0.982301\pi$
$614$	−351432.			−0.0376201
$615$		0			0
$616$	1.49658e6			0.158908
$617$			1.29854e7i			1.37323i	0.727020	+	0.686616i	$0.240905\pi$
$617$			1.29854e7i			1.37323i	−0.727020	+	0.686616i	$0.759095\pi$
$618$		0			0
$619$	−7.92002e6			−0.830806			−0.415403	−	0.909637i	$-0.636359\pi$
$619$	−7.92002e6			−0.830806			−0.415403	+	0.909637i	$0.636359\pi$
$620$	−1.80224e6	−	327680.i	−0.188293	−	0.0342350i
$621$		0			0
$622$			2.39741e6i			0.248465i
$623$			1.34632e7i			1.38972i
$624$		0			0
$625$	7.34562e6	+	6.43500e6i	0.752192	+	0.658944i
$626$	−8.37366e6			−0.854043
$627$		0			0
$628$			6.92973e6i			0.701160i
$629$	−8.95386e6			−0.902368
$630$		0			0
$631$	1.68218e7			1.68189			0.840945	−	0.541120i	$-0.181999\pi$
$631$	1.68218e7			1.68189			0.840945	+	0.541120i	$0.181999\pi$
$632$		−	2.25792e6i		−	0.224862i
$633$		0			0
$634$	−9.66501e6			−0.954947
$635$	−1.75238e6	+	9.63809e6i	−0.172462	+	0.948542i
$636$		0			0
$637$		−	5.57939e6i		−	0.544801i
$638$			159840.i			0.0155465i
$639$		0			0
$640$	163840.	−	901120.i	0.0158114	−	0.0869626i
$641$	1.55154e7			1.49148			0.745741	−	0.666236i	$-0.232096\pi$
$641$	1.55154e7			1.49148			0.745741	+	0.666236i	$0.232096\pi$
$642$		0			0
$643$			1.05801e7i			1.00916i	0.863364	+	0.504582i	$0.168354\pi$
$643$			1.05801e7i			1.00916i	−0.863364	+	0.504582i	$0.831646\pi$
$644$	−3.14989e6			−0.299282
$645$		0			0
$646$	−1.81862e7			−1.71460
$647$			1.37883e7i			1.29494i	0.762090	+	0.647471i	$0.224173\pi$
$647$			1.37883e7i			1.29494i	−0.762090	+	0.647471i	$0.775827\pi$
$648$		0			0
$649$	−5.88152e6			−0.548123
$650$	8.00280e6	+	3.00960e6i	0.742948	+	0.279399i
$651$		0			0
$652$		−	2.38614e6i		−	0.219825i
$653$			1.58924e6i			0.145850i	0.997337	+	0.0729248i	$0.0232333\pi$
$653$			1.58924e6i			0.145850i	−0.997337	+	0.0729248i	$0.976767\pi$
$654$		0			0
$655$	1.64809e7	+	2.99652e6i	1.50099	+	0.272907i
$656$	613888.			0.0556967
$657$		0			0
$658$			6.75102e6i			0.607862i
$659$	−9.12434e6			−0.818442			−0.409221	−	0.912435i	$-0.634199\pi$
$659$	−9.12434e6			−0.818442			−0.409221	+	0.912435i	$0.634199\pi$
$660$		0			0
$661$	6.50310e6			0.578918			0.289459	−	0.957190i	$-0.406525\pi$
$661$	6.50310e6			0.578918			0.289459	+	0.957190i	$0.406525\pi$
$662$			6.56379e6i			0.582116i
$663$		0			0
$664$	−1.78086e6			−0.156751
$665$	3.50760e6	−	1.92918e7i	0.307578	−	1.69168i
$666$		0			0
$667$		−	336420.i		−	0.0292797i
$668$			8.95363e6i			0.776351i
$669$		0			0
$670$	7.06156e6	+	1.28392e6i	0.607734	+	0.110497i
$671$	−6.26010e6			−0.536754
$672$		0			0
$673$		−	2.17810e6i		−	0.185370i	−0.995695	−	0.0926850i	$-0.970455\pi$
$673$		−	2.17810e6i		−	0.185370i	0.995695	−	0.0926850i	$-0.0295449\pi$
$674$	−8.75091e6			−0.741999
$675$		0			0
$676$	1.54501e6			0.130036
$677$			3.98419e6i			0.334094i	0.985949	+	0.167047i	$0.0534231\pi$
$677$			3.98419e6i			0.334094i	−0.985949	+	0.167047i	$0.946577\pi$
$678$		0			0
$679$	1.53627e7			1.27877
$680$	7.20896e6	+	1.31072e6i	0.597861	+	0.108702i
$681$		0			0
$682$			1.21242e6i			0.0998138i
$683$			5.91563e6i			0.485231i	0.970122	+	0.242616i	$0.0780054\pi$
$683$			5.91563e6i			0.485231i	−0.970122	+	0.242616i	$0.921995\pi$
$684$		0			0
$685$	1.07928e6	−	5.93604e6i	0.0878836	−	0.483360i
$686$	−5.46680e6			−0.443530
$687$		0			0
$688$			587264.i			0.0473001i
$689$	2.02738e6			0.162700
$690$		0			0
$691$	−1.55471e7			−1.23867			−0.619335	−	0.785127i	$-0.712598\pi$
$691$	−1.55471e7			−1.23867			−0.619335	+	0.785127i	$0.712598\pi$
$692$			5.50086e6i			0.436682i
$693$		0			0
$694$	1.09801e7			0.865379
$695$	−1.08053e7	−	1.96460e6i	−0.848545	−	0.154281i
$696$		0			0
$697$			4.91110e6i			0.382910i
$698$		−	1.06046e7i		−	0.823864i
$699$		0			0
$700$	−2.78080e6	+	7.39440e6i	−0.214499	+	0.570372i
$701$	2.27103e7			1.74553			0.872766	−	0.488139i	$-0.162324\pi$
$701$	2.27103e7			1.74553			0.872766	+	0.488139i	$0.162324\pi$
$702$		0			0
$703$		−	9.70584e6i		−	0.740704i
$704$	−606208.			−0.0460988
$705$		0			0
$706$	−1.22307e7			−0.923502
$707$		−	679084.i		−	0.0510946i
$708$		0			0
$709$	−6.29841e6			−0.470560			−0.235280	−	0.971928i	$-0.575601\pi$
$709$	−6.29841e6			−0.470560			−0.235280	+	0.971928i	$0.575601\pi$
$710$	−169920.	+	934560.i	−0.0126502	+	0.0695763i
$711$		0			0
$712$		−	5.45344e6i		−	0.403154i
$713$		−	2.55181e6i		−	0.187985i
$714$		0			0
$715$	1.01232e6	−	5.56776e6i	0.0740547	−	0.407301i
$716$	−383680.			−0.0279696
$717$		0			0
$718$		−	1.51742e7i		−	1.09849i
$719$	2.11911e7			1.52873			0.764367	−	0.644782i	$-0.223052\pi$
$719$	2.11911e7			1.52873			0.764367	+	0.644782i	$0.223052\pi$
$720$		0			0
$721$	1.96100e7			1.40488
$722$		−	9.80920e6i		−	0.700311i
$723$		0			0
$724$	1.04304e7			0.739526
$725$	−789750.	−	297000.i	−0.0558013	−	0.0209851i
$726$		0			0
$727$		−	1.35610e7i		−	0.951605i	−0.879552	−	0.475803i	$-0.842158\pi$
$727$		−	1.35610e7i		−	0.951605i	0.879552	−	0.475803i	$-0.157842\pi$
$728$			6.91661e6i			0.483687i
$729$		0			0
$730$	−6.62288e6	−	1.20416e6i	−0.459981	−	0.0836329i
$731$	−4.69811e6			−0.325185
$732$		0			0
$733$			2.69413e7i			1.85208i	0.377429	+	0.926038i	$0.376808\pi$
$733$			2.69413e7i			1.85208i	−0.377429	+	0.926038i	$0.623192\pi$
$734$	1.24424e7			0.852441
$735$		0			0
$736$	1.27590e6			0.0868207
$737$		−	4.75050e6i		−	0.322160i
$738$		0			0
$739$	−2.77414e6			−0.186860			−0.0934302	−	0.995626i	$-0.529783\pi$
$739$	−2.77414e6			−0.186860			−0.0934302	+	0.995626i	$0.529783\pi$
$740$	−699520.	+	3.84736e6i	−0.0469592	+	0.258276i
$741$		0			0
$742$			1.87325e6i			0.124907i
$743$		−	1.85538e7i		−	1.23299i	−0.787358	−	0.616497i	$-0.788551\pi$
$743$		−	1.85538e7i		−	1.23299i	0.787358	−	0.616497i	$-0.211449\pi$
$744$		0			0
$745$	−7.63675e6	−	1.38850e6i	−0.504101	−	0.0916548i
$746$	−5.66078e6			−0.372417
$747$		0			0
$748$		−	4.84966e6i		−	0.316926i
$749$	−6.69004e6			−0.435736
$750$		0			0
$751$	−2.19285e6			−0.141876			−0.0709380	−	0.997481i	$-0.522599\pi$
$751$	−2.19285e6			−0.141876			−0.0709380	+	0.997481i	$0.522599\pi$
$752$		−	2.73459e6i		−	0.176339i
$753$		0			0
$754$	−738720.			−0.0473207
$755$	−2.28884e7	−	4.16152e6i	−1.46133	−	0.265696i
$756$		0			0
$757$			9.48749e6i			0.601744i	0.953665	+	0.300872i	$0.0972777\pi$
$757$			9.48749e6i			0.601744i	−0.953665	+	0.300872i	$0.902722\pi$
$758$		−	1.56105e7i		−	0.986832i
$759$		0			0
$760$	−1.42080e6	+	7.81440e6i	−0.0892275	+	0.490752i
$761$	−9.69580e6			−0.606907			−0.303453	−	0.952846i	$-0.598140\pi$
$761$	−9.69580e6			−0.606907			−0.303453	+	0.952846i	$0.598140\pi$
$762$		0			0
$763$		−	5.68642e6i		−	0.353612i
$764$	3.24403e6			0.201072
$765$		0			0
$766$	−2.78270e6			−0.171354
$767$		−	2.71822e7i		−	1.66838i
$768$		0			0
$769$	−9.32787e6			−0.568809			−0.284405	−	0.958704i	$-0.591796\pi$
$769$	−9.32787e6			−0.568809			−0.284405	+	0.958704i	$0.591796\pi$
$770$	5.14448e6	+	935360.i	0.312690	+	0.0568528i
$771$		0			0
$772$			7.24250e6i			0.437366i
$773$			9.68080e6i			0.582723i	0.956613	+	0.291362i	$0.0941083\pi$
$773$			9.68080e6i			0.582723i	−0.956613	+	0.291362i	$0.905892\pi$
$774$		0			0
$775$	−5.99040e6	−	2.25280e6i	−0.358263	−	0.134731i
$776$	−6.22285e6			−0.370967
$777$		0			0
$778$		−	1.99316e6i		−	0.118057i
$779$	−5.32356e6			−0.314310
$780$		0			0
$781$	628704.			0.0368824
$782$			1.02072e7i			0.596886i
$783$		0			0
$784$	−2.08819e6			−0.121333
$785$	−4.33108e6	+	2.38209e7i	−0.250855	+	1.37970i
$786$		0			0
$787$			5.52302e6i			0.317863i	0.987290	+	0.158931i	$0.0508049\pi$
$787$			5.52302e6i			0.317863i	−0.987290	+	0.158931i	$0.949195\pi$
$788$		−	5.39949e6i		−	0.309768i
$789$		0			0
$790$	1.41120e6	−	7.76160e6i	0.0804490	−	0.442470i
$791$	3.61529e7			2.05448
$792$		0			0
$793$		−	2.89318e7i		−	1.63378i
$794$	−4.38267e6			−0.246711
$795$		0			0
$796$	−8.97600e6			−0.502112
$797$		−	1.71119e7i		−	0.954230i	−0.878841	−	0.477115i	$-0.841682\pi$
$797$		−	1.71119e7i		−	0.954230i	0.878841	−	0.477115i	$-0.158318\pi$
$798$		0			0
$799$	2.18767e7			1.21232
$800$	1.12640e6	−	2.99520e6i	0.0622254	−	0.165463i
$801$		0			0
$802$		−	9.96639e6i		−	0.547145i
$803$			4.45539e6i			0.243836i
$804$		0			0
$805$	−1.08277e7	−	1.96868e6i	−0.588909	−	0.107074i
$806$	−5.60333e6			−0.303814
$807$		0			0
$808$			275072.i			0.0148224i
$809$	−1.45309e7			−0.780586			−0.390293	−	0.920691i	$-0.627626\pi$
$809$	−1.45309e7			−0.780586			−0.390293	+	0.920691i	$0.627626\pi$
$810$		0			0
$811$	−2.13545e7			−1.14009			−0.570044	−	0.821614i	$-0.693074\pi$
$811$	−2.13545e7			−1.14009			−0.570044	+	0.821614i	$0.693074\pi$
$812$		−	682560.i		−	0.0363288i
$813$		0			0
$814$	2.58822e6			0.136912
$815$	1.49134e6	−	8.20237e6i	0.0786471	−	0.432559i
$816$		0			0
$817$		−	5.09268e6i		−	0.266926i
$818$		−	1.45340e7i		−	0.759453i
$819$		0			0
$820$	2.11024e6	+	383680.i	0.109597	+	0.0199267i
$821$	−3.67967e7			−1.90525			−0.952623	−	0.304154i	$-0.901626\pi$
$821$	−3.67967e7			−1.90525			−0.952623	+	0.304154i	$0.901626\pi$
$822$		0			0
$823$		−	3.30668e7i		−	1.70174i	−0.525376	−	0.850870i	$-0.676075\pi$
$823$		−	3.30668e7i		−	1.70174i	0.525376	−	0.850870i	$-0.323925\pi$
$824$	−7.94330e6			−0.407552
$825$		0			0
$826$	2.51157e7			1.28084
$827$			1.77309e7i			0.901505i	0.892649	+	0.450752i	$0.148844\pi$
$827$			1.77309e7i			0.901505i	−0.892649	+	0.450752i	$0.851156\pi$
$828$		0			0
$829$	−1.29375e7			−0.653830			−0.326915	−	0.945054i	$-0.606009\pi$
$829$	−1.29375e7			−0.653830			−0.326915	+	0.945054i	$0.606009\pi$
$830$	−6.12172e6	−	1.11304e6i	−0.308445	−	0.0560810i
$831$		0			0
$832$		−	2.80166e6i		−	0.140316i
$833$		−	1.67055e7i		−	0.834157i
$834$		0			0
$835$	−5.59602e6	+	3.07781e7i	−0.277756	+	1.52766i
$836$	5.25696e6			0.260147
$837$		0			0
$838$			1.45751e7i			0.716972i
$839$	3.31812e7			1.62738			0.813688	−	0.581302i	$-0.197457\pi$
$839$	3.31812e7			1.62738			0.813688	+	0.581302i	$0.197457\pi$
$840$		0			0
$841$	−2.04382e7			−0.996446
$842$			7.30119e6i			0.354906i
$843$		0			0
$844$	1.28888e7			0.622810
$845$	5.31096e6	+	965630.i	0.255877	+	0.0465231i
$846$		0			0
$847$			2.19852e7i			1.05299i
$848$		−	758784.i		−	0.0362350i
$849$		0			0
$850$	2.39616e7	+	9.01120e6i	1.13754	+	0.427795i
$851$	−5.44751e6			−0.257854
$852$		0			0
$853$		−	5.17224e6i		−	0.243392i	−0.992567	−	0.121696i	$-0.961167\pi$
$853$		−	5.17224e6i		−	0.243392i	0.992567	−	0.121696i	$-0.0388332\pi$
$854$	2.67323e7			1.25427
$855$		0			0
$856$	2.70989e6			0.126406
$857$		−	1.05320e7i		−	0.489845i	−0.969543	−	0.244922i	$-0.921238\pi$
$857$		−	1.05320e7i		−	0.489845i	0.969543	−	0.244922i	$-0.0787625\pi$
$858$		0			0
$859$	1.14741e7			0.530563			0.265282	−	0.964171i	$-0.414535\pi$
$859$	1.14741e7			0.530563			0.265282	+	0.964171i	$0.414535\pi$
$860$	−367040.	+	2.01872e6i	−0.0169226	+	0.0930743i
$861$		0			0
$862$			1.14174e7i			0.523359i
$863$		−	1.92722e7i		−	0.880856i	−0.897788	−	0.440428i	$-0.854827\pi$
$863$		−	1.92722e7i		−	0.880856i	0.897788	−	0.440428i	$-0.145173\pi$
$864$		0			0
$865$	−3.43804e6	+	1.89092e7i	−0.156232	+	0.859277i
$866$	−2.35110e6			−0.106531
$867$		0			0
$868$		−	5.17734e6i		−	0.233243i
$869$	−5.22144e6			−0.234553
$870$		0			0
$871$	2.19550e7			0.980593
$872$			2.30336e6i			0.102582i
$873$		0			0
$874$	−1.10645e7			−0.489951
$875$	−1.41805e7	+	2.36802e7i	−0.626140	+	1.04560i
$876$		0			0
$877$		−	2.30524e7i		−	1.01208i	−0.862509	−	0.506042i	$-0.831108\pi$
$877$		−	2.30524e7i		−	1.01208i	0.862509	−	0.506042i	$-0.168892\pi$
$878$			2.44642e7i			1.07101i
$879$		0			0
$880$	−2.08384e6	−	378880.i	−0.0907105	−	0.0164928i
$881$	−2.26690e7			−0.983994			−0.491997	−	0.870597i	$-0.663733\pi$
$881$	−2.26690e7			−0.983994			−0.491997	+	0.870597i	$0.663733\pi$
$882$		0			0
$883$			3.67337e6i			0.158549i	0.996853	+	0.0792745i	$0.0252604\pi$
$883$			3.67337e6i			0.158549i	−0.996853	+	0.0792745i	$0.974740\pi$
$884$	2.24133e7			0.964662
$885$		0			0
$886$	9.43082e6			0.403613
$887$			3.39649e7i			1.44951i	0.689007	+	0.724755i	$0.258047\pi$
$887$			3.39649e7i			1.44951i	−0.689007	+	0.724755i	$0.741953\pi$
$888$		0			0
$889$	−2.76876e7			−1.17498
$890$	3.40840e6	−	1.87462e7i	0.144237	−	0.793301i
$891$		0			0
$892$		−	1.94969e7i		−	0.820451i
$893$			2.37140e7i			0.995123i
$894$		0			0
$895$	−1.31890e6	−	239800.i	−0.0550369	−	0.0100067i
$896$	2.58867e6			0.107723
$897$		0			0
$898$		−	2.19894e7i		−	0.909960i
$899$	552960.			0.0228189
$900$		0			0
$901$	6.07027e6			0.249113
$902$		−	1.41962e6i		−	0.0580971i
$903$		0			0
$904$	−1.46442e7			−0.595999
$905$	3.58544e7	+	6.51898e6i	1.45519	+	0.264581i
$906$		0			0
$907$			2.13327e7i			0.861050i	0.902579	+	0.430525i	$0.141672\pi$
$907$			2.13327e7i			0.861050i	−0.902579	+	0.430525i	$0.858328\pi$
$908$		−	9.02941e6i		−	0.363450i
$909$		0			0
$910$	−4.32288e6	+	2.37758e7i	−0.173049	+	0.951771i
$911$	1.03512e7			0.413235			0.206617	−	0.978422i	$-0.433754\pi$
$911$	1.03512e7			0.413235			0.206617	+	0.978422i	$0.433754\pi$
$912$		0			0
$913$			4.11825e6i			0.163507i
$914$	4.64157e6			0.183780
$915$		0			0
$916$	8.96528e6			0.353041
$917$			4.73450e7i			1.85931i
$918$		0			0
$919$	2.59019e7			1.01168			0.505839	−	0.862628i	$-0.331183\pi$
$919$	2.59019e7			1.01168			0.505839	+	0.862628i	$0.331183\pi$
$920$	4.38592e6	+	797440.i	0.170841	+	0.0310619i
$921$		0			0
$922$		−	9.21319e6i		−	0.356930i
$923$			2.90563e6i			0.112263i
$924$		0			0
$925$	−4.80920e6	+	1.27881e7i	−0.184807	+	0.491419i
$926$	1.08537e7			0.415960
$927$		0			0
$928$			276480.i			0.0105389i
$929$	−3.13230e7			−1.19076			−0.595379	−	0.803445i	$-0.702998\pi$
$929$	−3.13230e7			−1.19076			−0.595379	+	0.803445i	$0.702998\pi$
$930$		0			0
$931$	1.81085e7			0.684714
$932$		−	4.69722e6i		−	0.177134i
$933$		0			0
$934$	1.62020e7			0.607717
$935$	3.03104e6	−	1.66707e7i	0.113387	−	0.623628i
$936$		0			0
$937$			2.08461e7i			0.775667i	0.921729	+	0.387833i	$0.126776\pi$
$937$			2.08461e7i			0.775667i	−0.921729	+	0.387833i	$0.873224\pi$
$938$			2.02859e7i			0.752814i
$939$		0			0
$940$	1.70912e6	−	9.40016e6i	0.0630889	−	0.346989i
$941$	3.82929e7			1.40976			0.704878	−	0.709328i	$-0.251002\pi$
$941$	3.82929e7			1.40976			0.704878	+	0.709328i	$0.251002\pi$
$942$		0			0
$943$			2.98791e6i			0.109418i
$944$	−1.01734e7			−0.371568
$945$		0			0
$946$	1.35805e6			0.0493387
$947$		−	4.25088e7i		−	1.54029i	−0.637866	−	0.770147i	$-0.720183\pi$
$947$		−	4.25088e7i		−	1.54029i	0.637866	−	0.770147i	$-0.279817\pi$
$948$		0			0
$949$	−2.05911e7			−0.742189
$950$	−9.76800e6	+	2.59740e7i	−0.351153	+	0.933748i
$951$		0			0
$952$			2.07094e7i			0.740585i
$953$		−	3.91855e7i		−	1.39763i	−0.715302	−	0.698816i	$-0.753711\pi$
$953$		−	3.91855e7i		−	1.39763i	0.715302	−	0.698816i	$-0.246289\pi$
$954$		0			0
$955$	1.11514e7	+	2.02752e6i	0.395658	+	0.0719377i
$956$	−9.34784e6			−0.330801
$957$		0			0
$958$		−	2.24211e7i		−	0.789303i
$959$	1.70526e7			0.598749
$960$		0			0
$961$	−2.44348e7			−0.853495
$962$			1.19618e7i			0.416734i
$963$		0			0
$964$	9.02077e6			0.312645
$965$	−4.52656e6	+	2.48961e7i	−0.156477	+	0.860622i
$966$		0			0
$967$			1.84836e7i			0.635653i	0.948149	+	0.317827i	$0.102953\pi$
$967$			1.84836e7i			0.635653i	−0.948149	+	0.317827i	$0.897047\pi$
$968$		−	8.90541e6i		−	0.305468i
$969$		0			0
$970$	−2.13910e7	−	3.88928e6i	−0.729966	−	0.132721i
$971$	−3.95031e7			−1.34457			−0.672284	−	0.740294i	$-0.734686\pi$
$971$	−3.95031e7			−1.34457			−0.672284	+	0.740294i	$0.734686\pi$
$972$		0			0
$973$		−	3.10407e7i		−	1.05111i
$974$	−2.85267e7			−0.963506
$975$		0			0
$976$	−1.08283e7			−0.363861
$977$			3.29043e7i			1.10285i	0.834225	+	0.551425i	$0.185916\pi$
$977$			3.29043e7i			1.10285i	−0.834225	+	0.551425i	$0.814084\pi$
$978$		0			0
$979$	−1.26111e7			−0.420529
$980$	−7.17816e6	−	1.30512e6i	−0.238753	−	0.0434095i
$981$		0			0
$982$			2.35258e7i			0.778513i
$983$			2.65797e7i			0.877338i	0.898649	+	0.438669i	$0.144550\pi$
$983$			2.65797e7i			0.877338i	−0.898649	+	0.438669i	$0.855450\pi$
$984$		0			0
$985$	3.37468e6	−	1.85607e7i	0.110826	−	0.609544i
$986$	−2.21184e6			−0.0724538
$987$		0			0
$988$			2.42957e7i			0.791839i
$989$	−2.85832e6			−0.0929225
$990$		0			0
$991$	1.92964e7			0.624153			0.312077	−	0.950057i	$-0.398975\pi$
$991$	1.92964e7			0.624153			0.312077	+	0.950057i	$0.398975\pi$
$992$			2.09715e6i			0.0676629i
$993$		0			0
$994$	−2.68474e6			−0.0861858
$995$	−3.08550e7	−	5.61000e6i	−0.988025	−	0.179641i
$996$		0			0
$997$			5.12017e7i			1.63135i	0.578511	+	0.815674i	$0.303634\pi$
$997$			5.12017e7i			1.63135i	−0.578511	+	0.815674i	$0.696366\pi$
$998$			7.02840e6i			0.223373i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.6.c.a.19.1		2
3.2	odd	2		10.6.b.a.9.2	yes	2
4.3	odd	2		720.6.f.a.289.1		2
5.2	odd	4		450.6.a.w.1.1		1
5.3	odd	4		450.6.a.c.1.1		1
5.4	even	2	inner	90.6.c.a.19.2		2
12.11	even	2		80.6.c.c.49.1		2
15.2	even	4		50.6.a.c.1.1		1
15.8	even	4		50.6.a.e.1.1		1
15.14	odd	2		10.6.b.a.9.1	✓	2
20.19	odd	2		720.6.f.a.289.2		2
24.5	odd	2		320.6.c.b.129.1		2
24.11	even	2		320.6.c.a.129.2		2
60.23	odd	4		400.6.a.k.1.1		1
60.47	odd	4		400.6.a.c.1.1		1
60.59	even	2		80.6.c.c.49.2		2
120.29	odd	2		320.6.c.b.129.2		2
120.59	even	2		320.6.c.a.129.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.6.b.a.9.1	✓	2	15.14	odd	2
10.6.b.a.9.2	yes	2	3.2	odd	2
50.6.a.c.1.1		1	15.2	even	4
50.6.a.e.1.1		1	15.8	even	4
80.6.c.c.49.1		2	12.11	even	2
80.6.c.c.49.2		2	60.59	even	2
90.6.c.a.19.1		2	1.1	even	1	trivial
90.6.c.a.19.2		2	5.4	even	2	inner
320.6.c.a.129.1		2	120.59	even	2
320.6.c.a.129.2		2	24.11	even	2
320.6.c.b.129.1		2	24.5	odd	2
320.6.c.b.129.2		2	120.29	odd	2
400.6.a.c.1.1		1	60.47	odd	4
400.6.a.k.1.1		1	60.23	odd	4
450.6.a.c.1.1		1	5.3	odd	4
450.6.a.w.1.1		1	5.2	odd	4
720.6.f.a.289.1		2	4.3	odd	2
720.6.f.a.289.2		2	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	90.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -16.0000 q^{4} +(-55.0000 - 10.0000i) q^{5} -158.000i q^{7} +64.0000i q^{8} +O(q^{10})\)	\(q-4.00000i q^{2} -16.0000 q^{4} +(-55.0000 - 10.0000i) q^{5} -158.000i q^{7} +64.0000i q^{8} +(-40.0000 + 220.000i) q^{10} +148.000 q^{11} +684.000i q^{13} -632.000 q^{14} +256.000 q^{16} +2048.00i q^{17} -2220.00 q^{19} +(880.000 + 160.000i) q^{20} -592.000i q^{22} +1246.00i q^{23} +(2925.00 + 1100.00i) q^{25} +2736.00 q^{26} +2528.00i q^{28} -270.000 q^{29} -2048.00 q^{31} -1024.00i q^{32} +8192.00 q^{34} +(-1580.00 + 8690.00i) q^{35} +4372.00i q^{37} +8880.00i q^{38} +(640.000 - 3520.00i) q^{40} +2398.00 q^{41} +2294.00i q^{43} -2368.00 q^{44} +4984.00 q^{46} -10682.0i q^{47} -8157.00 q^{49} +(4400.00 - 11700.0i) q^{50} -10944.0i q^{52} -2964.00i q^{53} +(-8140.00 - 1480.00i) q^{55} +10112.0 q^{56} +1080.00i q^{58} -39740.0 q^{59} -42298.0 q^{61} +8192.00i q^{62} -4096.00 q^{64} +(6840.00 - 37620.0i) q^{65} -32098.0i q^{67} -32768.0i q^{68} +(34760.0 + 6320.00i) q^{70} +4248.00 q^{71} +30104.0i q^{73} +17488.0 q^{74} +35520.0 q^{76} -23384.0i q^{77} -35280.0 q^{79} +(-14080.0 - 2560.00i) q^{80} -9592.00i q^{82} +27826.0i q^{83} +(20480.0 - 112640. i) q^{85} +9176.00 q^{86} +9472.00i q^{88} -85210.0 q^{89} +108072. q^{91} -19936.0i q^{92} -42728.0 q^{94} +(122100. + 22200.0i) q^{95} +97232.0i q^{97} +32628.0i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{4} - 110 q^{5}+O(q^{10}) \) 2 * q - 32 * q^4 - 110 * q^5	\( 2 q - 32 q^{4} - 110 q^{5} - 80 q^{10} + 296 q^{11} - 1264 q^{14} + 512 q^{16} - 4440 q^{19} + 1760 q^{20} + 5850 q^{25} + 5472 q^{26} - 540 q^{29} - 4096 q^{31} + 16384 q^{34} - 3160 q^{35} + 1280 q^{40} + 4796 q^{41} - 4736 q^{44} + 9968 q^{46} - 16314 q^{49} + 8800 q^{50} - 16280 q^{55} + 20224 q^{56} - 79480 q^{59} - 84596 q^{61} - 8192 q^{64} + 13680 q^{65} + 69520 q^{70} + 8496 q^{71} + 34976 q^{74} + 71040 q^{76} - 70560 q^{79} - 28160 q^{80} + 40960 q^{85} + 18352 q^{86} - 170420 q^{89} + 216144 q^{91} - 85456 q^{94} + 244200 q^{95}+O(q^{100}) \) 2 * q - 32 * q^4 - 110 * q^5 - 80 * q^10 + 296 * q^11 - 1264 * q^14 + 512 * q^16 - 4440 * q^19 + 1760 * q^20 + 5850 * q^25 + 5472 * q^26 - 540 * q^29 - 4096 * q^31 + 16384 * q^34 - 3160 * q^35 + 1280 * q^40 + 4796 * q^41 - 4736 * q^44 + 9968 * q^46 - 16314 * q^49 + 8800 * q^50 - 16280 * q^55 + 20224 * q^56 - 79480 * q^59 - 84596 * q^61 - 8192 * q^64 + 13680 * q^65 + 69520 * q^70 + 8496 * q^71 + 34976 * q^74 + 71040 * q^76 - 70560 * q^79 - 28160 * q^80 + 40960 * q^85 + 18352 * q^86 - 170420 * q^89 + 216144 * q^91 - 85456 * q^94 + 244200 * q^95

Introduction

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